The global character of solutions of an anti-competitive system of rational difference equations

In this paper, we analyze the global character of the solutions of an anti-competitive system of rational difference equations. We prove that the solutions of the system can have three different types of global behavior, corresponding to different regions of the parameter space. Our analysis utilizes a global convergence theorem from Camouzis and Ladas, and two theorems from Kulenović and Merino that apply to competitive systems.